Module:Infobox ET
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local p = {}
local utils = require("Module:Utils")
local rat = require("Module:Rational")
local limits = require("Module:Limits")
local ET = require("Module:ET")
local infobox = require("Module:Infobox")
-- check whether the input is a non-empty string
local function value_provided(s)
return type(s) == "string" and #s > 0
end
-- towards is one of: -1 (floor), 0 (nearest), 1 (ceil)
local function approximation(et, interval, towards, precomputed_approx)
local approx = precomputed_approx or ET.approximate(et, interval, towards or 0)
local tuning = et.size
if not rat.eq(et.equave, 2) then
tuning = tuning .. et.suffix
end
local ratio = rat.new(approx, et.size)
local convergement_notice = ""
local converges = rat.converges(ratio, math.log(interval) / math.log(rat.as_float(et.equave)))
if converges then
convergement_notice = "<br/>(" .. converges .. ")"
end
if rat.as_table(ratio)[1] ~= approx then
convergement_notice = ""
local link = rat.as_table(ratio)[2] .. et.suffix
ratio = " (→[[" .. link .. "|" .. rat.as_ratio(ratio, "\\")
if not rat.eq(et.equave, 2) then
ratio = ratio .. et.suffix
end
ratio = ratio .. "]])"
else
ratio = ""
end
local cents = utils._round(ET.cents(et, approx), 6)
return approx .. "\\" .. tuning .. " (" .. cents .. "¢)" .. ratio .. convergement_notice
end
function p.infobox_ET(frame)
-- debug mode will disable the categories
local debug_mode = frame.args["debug"]
local categories = ""
local tuning = frame.args["tuning"]
local et = ET.parse(tuning) or ET.parse("12edo")
-- category of the main article
categories = categories .. "[[Category:" .. tuning .. "| ]]"
-- category of the equal division
if rat.eq(et.equave, 2) then
categories = categories
.. "[[Category:Equal divisions of the octave|"
.. string.rep("#", string.len(et.size))
.. "]]"
else
categories = categories .. "[[Category:" .. et.suffix .. "|" .. string.rep("#", string.len(et.size)) .. "]]"
end
-- prime factorization
local prime_factorization_override = frame.args["Prime factorization"]
local prime_factorization
if not value_provided(prime_factorization_override) then
prime_factorization = utils._prime_factorization(et.size)
if utils.is_prime(et.size) then
prime_factorization = prime_factorization .. " (prime)"
if rat.eq(et.equave, 2) then
categories = categories .. "[[Category:Prime EDO|" .. string.rep("#", string.len(et.size)) .. "]]"
end
end
else
prime_factorization = prime_factorization_override
end
-- zeta test
local zeta_override = frame.args["Zeta"]
local zeta_switch
if value_provided(zeta_override) then
zeta_switch = not zeta_override:match("^[Nn][Oo]$")
else
zeta_switch = rat.eq(et.equave, 2) and ET.is_zeta(et)
end
-- navigation arrows
local increment = 1
if rat.eq(et.equave, 9 / 4) or rat.eq(et.equave, 4) or rat.eq(et.equave, 9) then
increment = 2
end
local prev_one = ""
if et.size >= increment then
prev_one = "[[" .. (et.size - increment) .. et.suffix .. "|← " .. (et.size - increment) .. et.suffix .. "]]"
end
local next_one = "[[" .. (et.size + increment) .. et.suffix .. "|" .. (et.size + increment) .. et.suffix .. " →]]"
-- step size
local step_size = ET.cents(et, 1)
local note_12edo = ""
if rat.eq(et.equave, 2) and et.size == 12 then
note_12edo = "<sup>by definition</sup>"
end
-- octave, twelfth, and fifth sizes
local octave = ET.approximate(et, 2)
local twelfth = ET.approximate(et, 3)
local fifth = -octave + twelfth -- 3/2 = [-1 1>
local fifth_error = ET.cents(et, fifth) - rat.cents(rat.new(3, 2))
local dual_fifth = math.abs(fifth_error) > step_size / 3
local A1 = -11 * octave + 7 * twelfth -- 2187/2048 = [-11 7>
local m2 = 8 * octave - 5 * twelfth -- 256/243 = [8 -5>
local A1_cents = utils._round(ET.cents(et, A1), 4)
local m2_cents = utils._round(ET.cents(et, m2), 4)
-- display
local infobox_data = {}
table.insert(infobox_data, {
"Prime factorization",
prime_factorization,
})
table.insert(infobox_data, {
"Step size",
utils._round(step_size, 6) .. "¢" .. note_12edo,
})
if not rat.eq(et.equave, 2) then
table.insert(infobox_data, {
"Octave",
approximation(et, 2),
})
if not rat.eq(et.equave, 3) then
table.insert(infobox_data, {
"Twelfth",
approximation(et, 3),
})
end
else
table.insert(infobox_data, {
"Fifth",
approximation(et, 3 / 2),
})
table.insert(infobox_data, {
"Semitones (A1:m2)",
A1 .. ":" .. m2 .. " (" .. A1_cents .. "¢ : " .. m2_cents .. "¢)",
})
if dual_fifth and et.size > 0 then
table.insert(infobox_data, {
"Dual sharp fifth",
approximation(et, 3 / 2, 1),
})
table.insert(infobox_data, {
"Dual flat fifth",
approximation(et, 3 / 2, -1),
})
local sharp = ET.approximate(et, 3 / 2, 1)
local flat = ET.approximate(et, 3 / 2, -1)
table.insert(infobox_data, {
"Dual major 2nd",
approximation(et, 9 / 8, 0, sharp + flat - octave),
})
categories = categories
.. "[[Category:Dual-fifth temperaments|"
.. string.rep("#", string.len(et.size))
.. "]]"
end
end
local consistency = tonumber(frame.args["Consistency"])
if consistency == nil then
consistency = limits.consistency_limit(et, false, 43)
end
if consistency == nil then
consistency = "at least 43"
end
if consistency ~= nil then
table.insert(infobox_data, {
"Consistency limit",
consistency,
})
end
local distinct_consistency = tonumber(frame.args["Distinct consistency"])
if distinct_consistency == nil then
distinct_consistency = limits.consistency_limit(et, consistency or true, 43)
end
if distinct_consistency == nil then
distinct_consistency = "at least 43"
end
if distinct_consistency ~= nil then
table.insert(infobox_data, {
"Distinct consistency limit",
distinct_consistency,
})
end
-- special properties
if ET.is_highly_composite(et) or zeta_switch then
local text = ""
if ET.is_highly_composite(et) then
text = text .. "[[Highly composite equal division|highly composite]]"
if rat.eq(et.equave, 2) then
categories = categories
.. "[[Category:Highly composite EDO|"
.. string.rep("#", string.len(et.size))
.. "]]"
end
end
if zeta_switch then
if #text > 0 then
text = text .. "<br>"
end
if not value_provided(zeta_override) then
text = text .. ET.why_zeta(et)
else
text = text .. zeta_override
end
categories = categories .. "[[Category:Zeta|" .. string.rep("#", string.len(et.size)) .. "]]"
end
table.insert(infobox_data, {
"Special properties",
'<div style="max-width: 270px;">' .. text .. "</div>",
})
end
local result = infobox.build("[[" .. et.suffix .. "|" .. tuning .. "]]", infobox_data, prev_one, next_one)
if not value_provided(debug_mode) then
result = result .. categories
end
return result
end
return p